Cascade self-seeding scheme with wake monochromator for narrow-bandwidth X-ray FELs
aa r X i v : . [ phy s i c s . acc - ph ] J un DEUTSCHES ELEKTRONEN-SYNCHROTRON
Ein Forschungszentrum der Helmholtz-Gemeinschaft
DESY 10-080June 2010
Cascade self-seeding scheme with wakemonochromator for narrow-bandwidth X-ray FELs
Gianluca Geloni,
European XFEL GmbH, Hamburg
Vitali Kocharyan and Evgeni Saldin
DeutschesElektronen-Synchrotron DESY, HamburgISSN 0418-9833
NOTKESTRASSE 85 - 22607 HAMBURG ascade self-seeding scheme with wakemonochromator for narrow-bandwidth X-rayFELs
Gianluca Geloni, a , Vitali Kocharyan b and Evgeni Saldin b a European XFEL GmbH, Hamburg, Germany b Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
Three di ff erent approaches have been proposed so far for production of highlymonochromatic X-rays from a baseline XFEL undulator: (i) single-bunch self-seeding scheme with a four crystal monochromator in Bragg reflection geometry;(ii) double-bunch self-seeding scheme with a four-crystal monochromator in Braggreflection geometry; (iii) single-bunch self-seeding scheme with a wake monochro-mator. A unique element of the X-ray optical design of the last scheme is themonochromatization of X-rays using a single crystal in Bragg-transmission geome-try. A great advantage of this method is that the monochromator introduces no pathdelay of X-rays. This fact eliminates the need for a long electron beam bypass, or forthe creation of two precisely separated, identical electron bunches, as required in theother two self-seeding schemes. In its simplest configuration, the self-seeded XFELconsists of an input undulator and an output undulator separated by a monochro-mator. In some experimental situations this simplest two-undulator configurationis not optimal. The obvious and technically possible extension is to use a setupwith three or more undulators separated by monochromators. This amplification-monochromatization cascade scheme is distinguished, in performance, by a smallheat-loading of crystals and a high spectral purity of the output radiation. Thispaper describes such cascade self-seeding scheme with wake monochromators. Wepresent feasibility study and exemplifications for the SASE2 line of the EuropeanXFEL. Introduction
The self-seeding approach in Free-Electron Lasers (FELs) was proposed toobtain a bandwidth narrower than that achievable with conventional X-raySASE schemes [1]-[5]. A self-seeded FEL consists of two undulators witha monochromanor located between them. In the original VUV-soft X-raycase, a grating monochromator was proposed [6]. Three types of self-seedingschemes for hard X-ray FELs have been studied [7]-[10]. Historically, the firsttype was a single bunch self seeding scheme with a four-crystal monochro-mator in Bragg reflection geometry [7]. A second type was the double bunchself-seeding scheme with four crystal monochromator in Bragg reflectiongeometry [8, 9], and a third type was a single-bunch self-seeding schememaking use of a wake monochromator [10]. A unique element of the X-ray optical design of the last scheme is the monochromatization of X-raysusing a single crystal in Bragg transmission geometry. The X-ray beam istransmitted through a thick crystal oriented for Bragg reflection. A greatadvantage of this method is that it introduces no path-delay of X-rays in themonochromator, thus avoiding the need for a long electron beam bypass,or for the creation of two precisely separated, identical electron bunches, asrequired in schemes with the monochromator in Bragg reflection geometry.In [10] we discussed how such kind of self-seeding scheme may be combinedwith a fresh bunch technique [11]-[16]. The combination of self-seeding andfresh bunch techniques is extremely insensitive to noise and non-ideal ef-fects. In fact, the radiation pulse used to produce the monochromatic (wake)seed signal is in the GW-level power. This large power can tremendouslyimprove the signal-to-noise ratio of the self-seeding scheme. The possibilityof combining self-seeding scheme and fresh bunch technique would be ofgreat importance especially during the early experimental stage, when aproof of principle is built.Despite of these advantages, the combination of self-seeding and freshbunch techniques su ff ers from two drawbacks. First, there is a strong SASEsignal outside of the seed bandwidth, due to application of fresh bunchtechnique . Second, the power of the SASE pulse which impinges on thecrystal is relatively large and heat-loading problems are not automaticallyavoided. This is the case, in particular, when the combination of self-seedingand fresh bunch techniques is used at the European XFEL, which is char-acterized by a very high repetition rate. These drawbacks can be overcomeby using the cascade self-seeding scheme proposed in the present work. Actually this can be transformed into an advantage. The SASE pulse can beseparated from the longitudinally coherent seed pulse by the post monochromatorin the experimental hall and exploited separately. ig. 1. Installation of a wake monochromator in the baseline XFEL undulator. Thesetup is composed of two components, a crystal and a weak magnetic chicane. Themagnetic chicane accomplishes three tasks by itself. It creates an o ff set for crys-tal installation, it removes the electron micro-bunching produced in the upstreamundulator, and it acts as a delay line for temporal windowing. The transmittancespectrum of the crystal shows a narrow-band absorption resonance when the inci-dent X-ray beam satisfies the Bragg di ff raction condition. The temporal waveformof the transmitted radiation pulse is characterized by a long monochromatic wake.After the crystal, the monochromatic wake of the radiation pulse is combined withthe delayed electron bunch, and amplified in the downstream undulator. In this paper we study such scheme, which consists of two parts: a suc-cession of two amplification-monochromatization cascades and an outputundulator in which the monochromatic seed signal is amplified up to satu-ration. Each cascade consists of an undulator, acting as an amplifier, and amonochromator.In the next section we describe in detail the method and the basic principlesof our technique. Subsequently, in the following sections, we study thefeasibility of the technique, giving exemplification for the SASE2 beamlineat the European XFEL.
The self-seeding technique considered in this work is based on the substitu-tion of a single undulator module with a weak chicane and a single crystal,4 ig. 2. Design of an undulator system for narrow-bandwidth mode of operation.The scheme is based on the use of a cascade, single bunch self-seeding scheme withwake monochromators. In performance, the cascade type of self-seeded XFEL isdistinguished by its small heat-loading of monochromators.Fig. 3. First cascade. Short pulse mode of operation. The crystal acts as a bandstopfilter for the transmitted X-ray SASE radiation pulse. as shown in Fig. 1. Two cascades can be arranged sequentially as shown inFig. 2. In this paper we will consider both the case when a single cascadeor two cascades are present. With reference to Fig. 2, we begin to study thecase when two-cascades are present.5he first undulator in Fig. 2 operates in the linear high-gain regime start-ing from the shot-noise in the electron beam. After the first undulator, theoutput SASE radiation passes through the monochromator, which reducesthe bandwidth to the desired value. According to the wake monochromatorprinciple, the SASE pulse coming from the first undulator impinges on acrystal set for Bragg di ff raction. Then, the single crystal in Bragg geome-try actually operates as a bandstop filter for the transmitted X-ray SASEradiation pulse, as shown in Fig. 3. When the incident angle and the spec-tral contents of the incoming beam satisfy the Bragg di ff raction condition,the temporal waveform of the transmitted radiation pulse shows a longmonochromatic wake. The duration of this wake is inversely proportionalto the bandwidth of the absorption line in the transmittance spectrum.While the radiation is sent through the crystal, the electron beam passesthrough a magnetic chicane, which accomplishes three tasks by itself: itcreates an o ff set for the crystal installation, it removes the electron micro-bunching produced in the first undulator, and it acts as a delay line for theimplementation of the temporal windowing. In other words, the magneticchicane shifts the electron bunch on top of the monochromatic wake createdby the bandstop filter thus selecting (temporal windowing) a part of thewake. By this, the electron bunch is seeded with a radiation pulse charac-terized by a bandwidth much narrower than the natural FEL bandwidth.For the hard X-ray wavelength range, a small dispersive strength R inthe order of ten microns is su ffi cient to remove the micro bunching in theelectron bunch. As a result, the choice of the strength of the magnetic chicaneonly depends on the delay that we want to introduce between electronbunch and radiation. In our case, this amounts to 6 µ m for the short pulsemode of operation and to 60 µ m for the long pulse mode of operation. Suchdispersion strength is small enough to be generated by a short 5 m-longchicane to be installed in place of a single undulator module. Such chicaneis, however, strong enough to create a su ffi ciently large transverse o ff set ofa few millimeters for installing the crystal.Successful operation of the self-seeded XFEL requires fulfillment of severalrequirements. The first undulator must operate in the deep linear regime,and not in saturation. In fact, the amplification process in the FEL leadsto an energy modulation in the electron beam. After the electron beampasses through the magnetic chicane, such energy modulation transformsinto additional energy spread. Calculations show that in order not to spoilthe electron beam quality, the power gain of the first undulator should beabout three orders of magnitude smaller than the power gain of the X-raySASE FEL at saturation. Here we consider the hard X-ray mode of operation,where the e ff ective power of shot-noise in the electron beam is P n ∼ P sat ∼
30 GW. It follows6hat for e ff ective operation of the second undulator, one requires that thepower gain of the first undulator be no more than four orders of magnitude.To provide e ff ective operation of the self-seeded XFEL, we also require thatthe power of the monochromatic seed signal P seed at the entrance of theoutput undulator significantly exceeds the e ff ective shot-noise power inthe electron beam, i.e. P seed ≫ P n . Calling G the power gain in the firstundulator, and T m the transmission factor of the monochromator one has P seed1 / P n ∼ G T m . For a bandpass filer the transmission factor is simply theratio of the of the transmitted pulse power to the incoming pulse power.Similarly, for the wake monochromator we can define T m as the ratio ofthe wake power in the temporal window defined by the electron bunchlength to the incoming pulse power. More in detail, T m can be written theproduct of a geometrical factor R m and a coe ffi cient K s , i.e. T m ∼ R m K s . Thegeometrical factor R m depends on the line width of the bandstop filter, ∆ ω m ,and on the time delay τ d , while the coe ffi cient K s can be written in theform K s ∼ ∆ ω m / ( ∆ ω in ), where ∆ ω in is the bandwidth of the incoming X-raybeam. Using only a single cascade, i.e. considering the simplest possibletwo-undulator configuration of the self-seeded XFEL, the bandwidth of theincoming beam is actually the radiation bandwidth of the SASE XFEL i.e. ∆ ω in ∼ ∆ ω SASE . Our calculations (see the next Sections) show that in thiscase the transmission factor for the wake monochromator is about 0 . P seed1 / P n ∼ G T m , and that G . , one cannot fulfillthe requirement P seed1 ≫ P n . In [10] we proposed a method to get aroundthis obstacle. It is based on the application of the self-seeding scheme withwake monochromator described above in combination with a fresh bunchtechnique. At variance, here we propose a new method to increase thevalue of P seed . A high value of the signal-to-noise ratio at the entrance of theoutput undulator may in fact be obtained by using more than one stage ofamplification-monochromatization.Consider the three-undulators self-seeding scheme (i.e. two cascades) asshown in Fig. 2. To be specific, here we consider the case of two identicalcascades. As discussed above, the signal-to-noise ratio at the entrance ofthe second undulator cannot be much larger than unity. Nevertheless, themonochromatic field amplitude at the entrance of the third undulator willbe much larger than that at the entrance of the second. The di ff erence withrespect to the previously discussed two-undulator configuration is that afteramplification in the second undulator, Fig. 4, the bandwidth of the X-raypulse related with the monochromatic signal that impinges on the secondcrystal is near to the transform-limited bandwidth of the electron bunch i.e. c /σ e . In other words, the transmission factor is now T m = R m ∆ ω m c /σ e . As aresult, assuming the same amplification G = G , the signal to noise ratio isenhanced by a factor given by the ratio of the two transmission factors, i.e. σ e ∆ ω SASE / c . A rough estimate for the signal to noise ratio at the entrance of7 ig. 4. Second cascade. The crystal acts as a bandstop filter for the self-seeded X-raypulse. The incident angles of first and second crystals are identical. The rotationerror must be smaller than 0 . the third (output) undulator is therefore P seed2 / P n ∼ ( P seed1 / P n ) σ e ∆ ω SASE / c ≫
1. Since this value is much larger than unity, we conclude that a doublecascade self-seeding scheme using a wake monochromator is insensitive tonoise and non-ideal e ff ects.It should be noted that the three-undulator configuration in Fig. 2 can benaturally taken advantage of in di ff erent schemes, as shown in Fig. 5. Theupper figure (a) shows the present self-seeding scheme. The middle figure(b) refers to the self-seeding scheme in combination with the fresh-bunchtechnique, as discussed in [10]. Finally, the lower figure (c) shows the advan-tage of a two-chicane setup when dealing with pump-probe techniques. Inthis case, as considered in [14], the first chicane enforces a fresh bunch tech-nique and prepares a radiation pulse of a given color while, the second canbe used to delay the electron bunch relative to such pulse, to obtain a tunabledelay. The three above-mentioned setups are now combined in a single unitcomposed by three undulators equipped with two wake monochromators.Finally, it is interesting to briefly discuss the simpler two-undulator con-figuration, Fig. 6. The two-undulator configuration may be particularly ad-vantageous in cases when the total available undulator length is too short8 ig. 5. Three modes of operation for the two weak magnetic chicanes installed inthe XFEL baseline undulator with tunable gap are foreseen. to enforce the three-undulator configuration. In this case, one may consideran increase in length of the first undulator in order to increase the contrastbetween seeded and SASE signal, at the cost of increasing the heat load.As discussed above, in the two-undulator configuration, even if the in-stantaneous powers of seed signal and SASE noise are comparable, in theFourier domain there is an enhance in photon spectral density order of σ e ∆ ω SASE / c >>
1, because of the di ff erent spectral widths of seed and SASEnoise. As a result, even though we have no spectral purity, in the case oftwo-undulator configuration the spectral density is still comparable with thethree-undulator configuration. If it is possible to use a post-monochromatorto filter out the SASE signal, a user will obtain a radiation source with char-acteristics comparable to the three-undulator configuration, with larger fluc-tuations and a few times smaller brightness. Spectral purity can be, however,of crucial importance for application of some other techniques like taper-ing and polarization manipulations, i.e. for the next steps of performanceimprovement. In a previous paper of us [10] we proposed to couple the monochromati-zation through a wake monochromator with a fresh-bunch technique. As9 ig. 6. Self-seeding setup with wake monochromator. Two undulator configuration.Short pulse mode of operation. Compared with the two cascade case, where almostall photons radiated within the seed bandwidth, here there is strong output SASEradiation outside this bandwidth. noted above, this solution has advantages in terms of high signal to noiseratio, but also disadvantages, among which the presence of o ff -band SASEradiation, and a high heat-load of the monochromator crystal. For the Euro-pean XFEL, the combination of our self-seeding scheme with a fresh bunchtechnique, as proposed in [8], satisfies the heat loading restrictions for theaverage power density. In fact, we showed that the situation is not di ff erentcompared to third generation sources. However, the European XFEL di ff erscompared to third generation sources in the very specific time diagram,which foresees the production of about 10 trains of pulses per second, eachtrain consisting of about 3000 pulses. In this case, the average power densityalong a single pulse-train is the meaningful figure of merit, rather than theabove-mentioned average power density.The two-cascade setup drastically relaxes the heat load on the crystals, andeliminates the presence of the o ff -band SASE radiation, still retaining theadvantage of a high signal to noise ratio. The energy per bunch impingingon the second crystal, which bears the largest heat-load, can be estimatedas 150 nJ for the short bunch (1 µ m) mode of operation and 1 . µ J for thelong bunch (10 µ m) mode of operation (see Section 4, Fig. 16 and Section5, Fig. 30). Let us consider the long-bunch mode of operation, which posesthe most di ffi cult challenge. From the previous numbers, one can easilyestimate an average power of 50 mW (1 . µ J × / train ×
10 trains / s).10his corresponds to a normal incident power density of 20W / mm atthe position of the second monochromator, already an order of magnitudesmaller compared with the average power density at monochromators ofthird generation synchrotron sources.The average power within a single bunch train can be estimated by mul-tiplying the energy by about 3 · pulses composing a single train anddividing by the temporal duration of a train, which is 0 . . µ m, as before, weobtain a power density of about 3 kW / mm within a single train, at normalincidence. Such heat-load is orders of magnitude smaller than what is fore-seen at monochromators for the baseline SASE2, where a diamond crystalwith the same thickness (0 . Following the previous introduction of the proposed methods we report ona feasibility study of the single-bunch self-seeding scheme. This feasibilitystudy is performed with the help of the FEL code GENESIS 1.3 [17] runningon a parallel machine. In this section we will present the feasibility studyfor the short-pulse mode of operation (1 µ m rms) while, later on, we willcover the long-pulse mode of operation (10 µ m rms). We will treat boththe two-undulator as well as the three-undulator configuration. Parametersused in the simulations for the short pulse mode of operation are presentedin Table 1. For the long pulse mode of operations Table 1 is still valid, exceptfor a ten times larger charge (0 .
25 nC) and a ten times longer rms bunchlength. We present a statistical analysis consisting of 100 runs for both shortand long pulse mode of operation. We consider a transverse rms dimension of the bunch of about 20 µ m. Assuming,with some approximation, that radiation is distributed as the electron bunch, weobtain an area of 2 . · − mm . able 1Parameters for the short pulse mode of operation used in this paper.UnitsUndulator period mm 48K parameter (rms) - 2.516Wavelength nm 0.15Energy GeV 17.5Charge nC 0.025Bunch length (rms) µ m 1.0Normalized emittance mm mrad 0.4Energy spread MeV 1.5 | T | [nm] Fig. 7. Transmissivity (sigma polarization) relevant to the Bragg 400 di ff raction ofX-rays at 0 .
15 nm from a Diamond crystal with a thickness of 0 . After the first seven cells (42 m) the electron bunch is sent through theweak chicane, while radiation is filtered through a single diamond crystal.Here we use the C(400) Bragg reflection and we assume, as said before,that the crystal has a thickness of 0 . ,150090 0,150095 0,150100 0,150105 0,150110-10010 P ha s e S h i ft [ r ad ] [nm] Fig. 8. Minimal phase shift of the forward-di ff racted X-rays at 0 .
15 nm (sigmapolarization) relevant to the Bragg 400 di ff raction from a Diamond crystal with athickness of 0 . transmissivity function for the sigma-polarization component are shown inFig. 7 and Fig. 8, and were calculated as described in [10]. The profile of theradiation before the filter is shown in Fig. 9.As discussed above, and explained in detail in [10], the crystal acts as abandstop filter. The e ff ect is best shown by a comparison of the spectrabefore and after the filter, Fig. 10. Monochromatization does not take placein the frequency domain. At first glance, the passage through the bandstopfilter is only responsible for slight change in the power distribution alongthe pulse. However, a zoom of the vertical axis shows what we are interestedin: a long, monochromatic tail in the power distribution on the left side ofthe picture, Fig. 11.Following the first crystal, we consider two alternative schemes. First, atwo-undulator configuration, where the radiation from the first crystal isused to seed the electron bunch in an output undulator and, second, athree-undulator configuration where two monochromatization cascades areforeseen. Let us first consider the two-undulator configuration.With reference to Fig. 6, we optimized the length of the output undulator13 I[ A ] P [ W ] s[ m] Fig. 9. Short pulse mode of operation. Input power at the crystal, at the end of thefirst undulator, 7 cells long (42 m). The average input power is represented with asolid thick line. A typical shot is also shown with a solid thin line. The dashed lineillustrates the corresponding distribution of the electron beam current. to obtain maximal spectral power. The optimal length is found to be 12cells. In Fig. 12 and Fig. 13 we show, respectively, the average energy of thepulse as a function of the undulator length, and the rms deviation from theaverage . Fig. 14 and Fig. 15 show, instead, the output power and spectrum.An estimation of the SASE contribution can be done by evaluating the totalpower outside the spectral window shown with black straight lines in Fig.15 and dividing it by the total power in the pulse. Such ratio is about 14%.Obviously there is some ambiguity in the definition of the spectral window.Nevertheless, the ratio is weakly dependent on the choice of the windowwidth and one can take the over-mentioned figure as a rough estimation ofthe SASE contribution to the total pulse. As one may see, at the beginning of the undulator the fluctuations of energyper pulse apparently drop, see Fig. 13. This can be explained considering thefact that the Genesis output consists of the total power integrated over the fullgrid up to an artificial boundary, i.e. there is no spectral selection. Therefore, ourcalculations include a relatively large spontaneous emission background, whichhas a much larger spectral width with respect to the amplification bandwidth andwhich fluctuates negligibly from shot to shot. Since there is a long lethargy of theseeded radiation at the beginning of the FEL amplifier, one observes an apparentdecrease of fluctuations. Then, when lethargy ends, the seed pulse gets amplifiedand fluctuations e ff ectively return to about the same level as after monochromator. ,1497 0,1500 0,1503 0,1506 0,150901x10 P () [ A . U .] [nm] P () [ A . U .] [nm] Fig. 10. Short pulse mode of operation. Average output spectrum after the dia-mond crystal and typical shot (solid thick line and solid thin line respectively). Thebandstop e ff ect is clearly visible, and highlighted in the inset. For comparison, theaverage spectrum before the diamond crystal and a typical shot (dotted thick lineand dotted thin line respectively) is also shown.
10 -8 -6 -4 -2 0 2 4 6 8 100,06,0x10 P [ W ] s[ m] Fig. 11. Short pulse mode of operation. Power distribution before (dotted line) andafter (solid line) transmission through the crystal. The monochromatic tail due tothe transmission through the bandstop filter is evident on the left of the figure.
10 20 30 40 50 60 700,08,0x10 -5 -4 E [ J ] z[m] Fig. 12. Two-undulator configuration. Short pulse mode of operation. Averageenergy of the radiation pulse as a function of the second undulator length. r m s ene r g y f l u c t ua t i on s z[m] Fig. 13. Two-undulator configuration. Short pulse mode of operation. rms energydeviation from the average as a function of the second undulator length. P [ W ] s[ m] Fig. 14. Two-undulator configuration. Short pulse mode of operation. Average andtypical single-shot output power (respectively, thick and thin solid lines). ,15000 0,15005 0,15010 0,15015 0,150200,00E+0001,00E+0152,00E+0153,00E+015 P () [ A . U .] [nm] SASE contribution ~ 14% Fig. 15. Two-undulator configuration. Short pulse mode of operation. Average andtypical single-shot output spectrum (respectively, thick and thin solid lines). Anestimation of the SASE contribution can be done by evaluating the total poweroutside the spectral window shown with black straight lines and dividing it to thespectral power integrated over all the spectrum. I[ A ] P [ W ] s[ m] Fig. 16. Short pulse mode of operation, second monochromatization cascade. Inputpower at the second crystal, at the end of the second undulator, 7 cells long (42m). The average input power is represented with a solid thick line. A typical shotis also shown with a solid thin line. The dashed line illustrates the correspondingdistribution of the electron beam current.
As discussed before, the three-undulator configuration presents advantagesrelated to the high contrast between seeded and SASE signal. With referenceto Fig. 2 the second undulator is now shortened to 7 cells (corresponding to42 m), and followed by a second seeding stage. The input power impingingon the second crystal is shown in Fig. 16.As before, the e ff ect of the filter is best shown by a comparison of the spectrabefore and after the filter, Fig. 17. A long, monochromatic tail in the powerdistribution on the left side of Fig. 18 constitutes the time-domain e ff ect ofthe filtering procedure.It is interesting to discuss here a paradox which arises when one comparesthe average spectrum before the filter (dotted line in Fig. 17) and the averagespectrum after the filter in the first monochromatization cascade, Fig. 10.The bandstop filter e ff ect is visible in the inset of the latter figure, butafter amplification (dotted line in Fig. 17) it disappears, and no hole isvisible in the spectrum anymore. This leads to an apparent contradiction,because the radiation pulse simply passes through a linear amplifier, and20 ,1498 0,1499 0,1500 0,1501 0,1502 0,1503 0,1504 0,15050,02,0x10 P () [ A . U .] [nm] P () [ A . U .] [nm] Fig. 17. Short pulse mode of operation, second monochromatization cascade. Av-erage output spectrum after the second diamond crystal (solid thick line). Thebandstop e ff ect is clearly visible, and highlighted in the inset. For comparison, theaverage spectrum before the diamond crystal (dotted thick line) is also shown. the bandstop e ff ect should still be visible. The paradox is explained in termsof the windowing process. The monochromatic pulse at the exit of the firstfilter serves, in fact, as seed for the electron bunch, which is shorter than themonochromatic wake itself. The seeding field is e ff ectively sampled onlywithin the electron bunch. In other words, the temporal windowing processoperated by the electron bunch is equivalent to a spectral measurement overa time equal to the bunch duration σ e / c . The length of the monochromatictail of the electric field (see Fig. 11) is related to the bandwidth of the crystalby inverse proportionality and is about 1 / ∆ ω m . When the two bandwidthsare related by σ e / c ≪ / ∆ ω m , like in the short-pulse mode of operation,the windowing process in the time domain is equivalent to a convolution,in the frequency domain, of the seeding pulse and a window-like signalwith bandwith c /σ e ≫ ∆ ω m . It follows that the hole in the spectrum is notresolved or, in other words, that we are measuring the spectrum of theseed signal with an instrument (the electron bunch) which integrates overa temporal interval too short to obtain the proper resolution. The situationchanges when the bunch length increases. This is equivalent to an increasein resolution in the spectral measurement, and can be seen in Fig. 31, whichis the analogous of Fig. 17 for the long-pulse mode of operation. The electronbunch is not long enough to resolve the seed signal properly in the frequency21
10 -8 -6 -4 -2 0 2 4 6 8 1001x10 P [ W ] s[ m] Fig. 18. Short pulse mode of operation, second monochromatization cascade. Powerdistribution before (dotted line) and after (solid line) transmission through the sec-ond crystal. The monochromatic tail due to the transmission through the bandstopfilter is evident on the left of the figure. domain, but the first filtering process is still visible in the dotted spectrumbefore the second filter, due to a better spectral resolution.Following the second crystal, the radiation is used to seed once more theelectron bunch. Radiation is collected at the exit of a third undulator. Fig. 19and Fig. 20 respectively show the output power and spectrum for the three-undulator configuration, while in Fig. 21 and Fig. 22 we present, respectively,the rms deviation from the average and the average energy of the pulse asa function of the undulator length. Similarly as before, an estimation of theSASE contribution can be done by evaluating the total power outside thespectral window shown with black straight lines in Fig. 20, and dividing itby the spectral power integrated over all the spectrum yielding, as expected,a much smaller SASE contribution in the order of a percent.
Let us now consider the case of long pulse mode of operation. The setups forthe two-undulator configuration and for the three-undulator configuration22 P [ W ] s[ m] Fig. 19. Three-undulator configuration. Short pulse mode of operation. Averageand typical single-shot output power (respectively, thick and thin solid lines). are the same considered before, respectively in Fig. 6 and Fig. 2. As saidabove, for the long pulse mode of operations Table 1 is still valid, except fora ten times larger charge (0 .
25 nC) and a ten times longer rms bunch length(10 µ m). Similarly as before, we begin with the first monochromatization cascade.After the first seven cells (42 m) the electron bunch is sent through the weakchicane, while radiation is filtered through a single diamond crystal. Weuse the same crystal as before. The transmissivity function (modulus andphase) for the sigma-polarization component was already presented in Fig.7, and Fig.8. The profile of the radiation before the filter is shown in Fig. 23.The e ff ect is best shown by a comparison of the spectra before and afterthe filter, Fig. 24. A long, monochromatic tail in the power distributioncan be clearly seen on the left side of Fig. 25. Compared to the previouslydiscussed short pulse mode of operation, the seeding level is about an orderof magnitude smaller.Similarly as before, following the first crystal, we consider, first, a two-23 ,15000 0,15003 0,15006 0,15009 0,15012 0,15015 0,1501801x10 P () [ A . U .] [nm] SASE contribution ~ 1% Fig. 20. Three-undulator configuration. Short pulse mode of operation. Averageand typical single-shot output spectrum (respectively, thick and thin solid lines).An estimation of the SASE contribution can be done by evaluating the total poweroutside the spectral window shown with black straight lines and dividing it to thespectral power integrated over all the spectrum. undulator configuration and, second, a three-undulator configuration. Al-though the average power of the seed signal after the first crystal amountsonly to about 3 kW, the bunch length is now 10 times longer. Therefore, thecontrast in spectrum can be comparable with the two-undulator configura-tion in the short pulse scheme.Still with reference to Fig. 6, we optimized the length of the output undulatorto obtain maximal spectral power. As before, the optimal length is found tobe 12 cells. In Fig. 26 and Fig. 27 we show, respectively, the average energyof the pulse as a function of the undulator length, and the rms deviationfrom the average. Fig. 28 and Fig. 29 show, instead, the output power andspectrum. In the present case, an estimation of the SASE contribution yieldsan important SASE contribution in the order of 65%.As before, we should remark that the two-undulator configuration may beparticularly advantageous in cases when the total available undulator lengthis too short to enforce the three-undulator configuration. In this case, onemay consider an increase in length of the first undulator in order to increasethe contrast between seeded and SASE signal, at the cost of increasing theheat load. 24
10 20 30 40 50 60 700,00,10,20,30,40,50,60,70,80,91,0 r m s ene r g y f l u c t ua t i on s z [m] Fig. 21. Three-undulator configuration. Short pulse mode of operation. rms energydeviation from the average as a function of the third undulator length. -5 -4 E [ J ] z [m] Fig. 22. Three-undulator configuration. Short pulse mode of operation. Averageenergy of the radiation pulse as a function of the third undulator length.
30 -20 -10 0 10 20 300,08,0x10 I[ A ] P [ W ] s[ m] Fig. 23. Long pulse mode of operation. Input power at the crystal, at the end of thefirst undulator, 7 cells long (42 m). The average input power is represented with asolid thick line. A typical shot is also shown with a solid thin line. The dashed lineillustrates the corresponding distribution of the electron beam current. ,1497 0,1500 0,1503 0,1506 0,15090,05,0x10 P () [ A . U .] [nm] P () [ A . U .] [nm] Fig. 24. Long pulse mode of operation. Average output spectrum after the dia-mond crystal and typical shot (solid thick line and solid thin line respectively). Thebandstop e ff ect is clearly visible, and highlighted in the inset. For comparison, theaverage spectrum before the diamond crystal and a typical shot (dotted thick lineand dotted thin line respectively) is also shown.
100 -80 -60 -40 -20 0 20 40 60 80 1000,03,0x10 P [ W ] s[ m] Fig. 25. Long pulse mode of operation. Power distribution before (dotted line) andafter (solid line) transmission through the crystal. The monochromatic tail due tothe transmission through the bandstop filter is evident on the left of the figure.
20 40 60 800,05,0x10 -4 -3 E [ J ] z[m] Fig. 26. Two-undulator configuration. Long pulse mode of operation. Average en-ergy of the radiation pulse as a function of the second undulator length. r m s ene r g y f l u c t ua t i on s z[m] Fig. 27. Two-undulator configuration. Long pulse mode of operation. RMS pulseenergy fluctuations along the second undulator.
30 -20 -10 0 10 20 300,02,0x10 P [ W ] s[ m] Fig. 28. Two-undulator configuration. Long pulse mode of operation. Average andtypical single-shot output spectrum (respectively, thick and thin solid lines). ,15009 0,15010 0,15011 0,15012 0,150130,05,0x10 P () [ A . U .] [nm] SASE contribution ~ 65% Fig. 29. Two-undulator configuration. Long pulse mode of operation. Average andtypical single-shot output spectrum (respectively, thick and thin solid lines). Anestimation of the SASE contribution can be done by evaluating the total poweroutside the spectral window shown with black straight lines and dividing it to thespectral power integrated over all the spectrum.
30 -20 -10 0 10 20 3001x10 P [ W ] s[ m] Fig. 30. Long pulse mode of operation, second monochromatization cascade. Inputpower at the second crystal, at the end of the second undulator, 7 cells long (42m). The average input power is represented with a solid thick line. A typical shotis also shown with a solid thin line. The dashed line illustrates the correspondingdistribution of the electron beam current.
As in the short pulse mode of operation, the three-undulator configurationpresents advantages related to the high contrast between seeded and SASEsignal. With reference to Fig. 2 the second undulator is now shortened to 7cells (corresponding to 42 m), and followed by a second seeding stage. Theinput power impinging on the second crystal is shown in Fig. 30.As before, the e ff ect of the filter is best shown by a comparison of the spectrabefore and after the filter, Fig. 31. The long, monochromatic tail in the powerdistribution on the left side of Fig. 32 constitutes the time-domain e ff ect ofthe filtering procedure.Following the second crystal, the radiation is used to seed once more theelectron bunch. Radiation is collected at the exit of a third undulator. Fig. 33and Fig. 34 respectively show the output power and spectrum for the three-undulator configuration, while in Fig. 35 and Fig. 36 we present, respectively,the average energy of the pulse as a function of the undulator length, and therms deviation from the average. The SASE contribution is strongly reduced32 ,15006 0,15009 0,15012 0,15015 0,1501801x10 P () [ A . U .] [nm] P () [ A . U .] [nm] Fig. 31. Long pulse mode of operation, second monochromatization cascade. Av-erage output spectrum after the second diamond crystal (solid thick line). Thebandstop e ff ect is clearly visible, and highlighted in the inset. For comparison, theaverage spectrum before the diamond crystal (dotted thick line) is also shown. to a few percent. 33
100 -80 -60 -40 -20 0 20 40 60 80 10001x10 P [ W ] s[ m] Fig. 32. Long pulse mode of operation, second monochromatization cascade. Powerdistribution before (dotted line) and after (solid line) transmission through the sec-ond crystal. The monochromatic tail due to the transmission through the bandstopfilter is evident on the left of the figure.
30 -20 -10 0 10 20 3001x10 P [ W ] s[ m] Fig. 33. Three-undulator configuration. Long pulse mode of operation. Averageand typical single-shot output power (respectively, thick and thin solid lines). ,150100 0,150105 0,150110 0,1501150,07,0x10 SASE contribution ~ 4% P () [ A . U .] [nm] Fig. 34. Three-undulator configuration. Long pulse mode of operation. Averageand typical single-shot output spectrum (respectively, thick and thin solid lines).An estimation of the SASE contribution can be done by evaluating the total poweroutside the spectral window shown with black straight lines and dividing it to thespectral power integrated over all the spectrum.
15 30 45 60 750,04,0x10 -4 -4 -3 E [ J ] z[m] Fig. 35. Three-undulator configuration. Long pulse mode of operation. Averageenergy of the radiation pulse as a function of the third undulator length. r m s ene r g y f l u c t ua t i on s z[m] Fig. 36. Three-undulator configuration. Long pulse mode of operation. rms energydeviation from the average as a function of the third undulator length. Conclusions
The fundamental problem of reducing the line width of SASE X-ray FELsis solved by implementing a self-seeding technique. In the present work,we described how to avoid the poor longitudinal coherence of hard X-raySASE pulses. Quite surprisingly, monochromatization can be performed byan almost trivial setup composed of as few as two components: a weakchicane, and a single crystal. We have described techniques for reducingthe line width of the output X-ray beam down to 10 − , i.e. down to Fourier-Transform limit of the radiation pulse. We have shown how to achieve thismonochromatization with small heat-loading of monochromators, whichis crucial for the European XFEL. Many interesting applications can befound for these self-seeding techniques. However, in order keep this paperwithin a reasonable size, we did not discuss, here, possible applicationsof the proposed method, leading e.g. to further improvement of the XFELperformance. The proposed cascade self-seeding scheme based on the useof the wake monochromator is extremely compact and takes almost no costand time to be implemented. It can be straightforwardly installed in thebaseline undulator system of the European XFEL and is safe, in the sensethat it guarantees the baseline mode of operation. We are grateful to Massimo Altarelli, Reinhard Brinkmann, Serguei Molodtsovand Edgar Weckert for their support and their interest during the compila-tion of this work.
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